Maths 4.4Lesson outlineLesson 4 of 9 in Module 4
Partial Derivatives and the Gradient
Differentiate a function of several variables, and read the gradient as the direction of steepest increase.
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Learn
In this lesson10 parts
- 01Two weights at once
- 02Holding one variable fixed
- 03The gradient
- 04Steepest increase, perpendicular to the contour
- 05Three identities
- 06Checkpoint: the gradient so far
- 07The hero cars' error in two weights
- 08One step against the gradient
- 09The gradient in Python
- 10Recap, challenge, and next: curvature
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- partial derivative
- the derivative with respect to one variable, with every other variable held fixed |
∂(x² + 3y²)/∂x = 4at(2, 1) - gradient
- the vector of all the partial derivatives |
(4, 6) - contour
- a curve joining points where the function has the same value | the ellipse
x² + 3y² = 7 - directional derivative
- the slope of
fin the direction of a unit vectoru,∇f · u|6.4641at 30°
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.